Hybrid System Science Methods: Some Observations

Nathaniel Osgood

Using Modeling to Prepare for Changing Healthcare Needs

April 16, 2014

System Science Methodologies: Highly Complementary

•Different modeling methodologies seek to answer different types of questions •No one system science methodology offers a replacement for the others •Significant synergies can be secured by using combinations of methodologies to address the same problem

–As cross-checks on understanding where two or more can be applied

–Exploiting competitive advantages

Multi-Framework Modeling •We have found the use of multiple frameworks highly effective

–Co-evolving multiple models for •Cross-validation

•Asking different sorts of questions •Revealing new questions to answer

–Within a single model •Dealing with questions at different scales •Improving robustness of models •Allowing for representation & changing of factors that are otherwise ignored

High later growth

PLConsequence1

Low later growth

1-PLConsequence2

Expand capacity

High later growth

PLConsequence3

Low later growth

1-PLConsequence4

No expansion

High early growth

PE

High later growth

PLConsequence5

Low later growth

1-PLConsequence6

Expand capacity

High later growth

PLConsequence7

Low later growth

1-PLConsequence8

No expansion

Low early growth

1-PE

Expand capacity

High later growth

PLConsequence9

Low later growth

1-PLConsequence10

Expand capacity

High later growth

PLConsequence11

Low later growth

1-PLConsequence12

No expansion

High early growth

PE

High later growth

PLConsequence13

Low later growth

1-PLConsequence14

Expand capacity

High later growth

PLConsequence15

Low later growth

1-PLConsequence16

No Expansion

Low early growth

1-PE

No expansion

Initial Decision

Discrete Event

Modeling

Agent-Based

Modeling

Social Network Analysis

Decision Analysis

Reminder:Multiple Model Types

System Dynamics Normal and

Underweight

Weight

Overweight

Pregnant with GDM

History of GDMT2DM

Developing Obesity

Pregnant Normal

Weight Mothers

with No GDM

History

Completion of Pregnancy

to Non-Overweight State

Completion of GDM

Pregnancy

Women with History of

GDM Developing T2DM

Overweight Individuals Developing T2DM

Normal WeightIndividuals Developing

T2DM

Pregnant with

T2DM

New Pregnancies from

Mother with T2DMCompletion of Pregnancy for Mother with T2DM

Pregnant

Overweight

Mothers with No

GDM History

Pregnancies of

Overweight Women

Completion ofPregnancy to

Overweight State

Pregnancies ofNon-Overweight

Women

Pregnancies to Overweight

Mother Developing GDM

Pregnancies toNon-Overweight Mother

Developing GDM

Pregnant with

Pre-Existing History of

GDM

Pregnancies for

Women with GDM

Pregnancies DevelopingGDM from Mother with

GDM History

Completion of Non-GDMPregnancy for Woman with

History of GDM

Shedding Obesity

Pregnant WomenDeveloping PersistentOverweight/Obesity

Oveweight Babies Born

from T2DM Mothers

Pregnant Women with GDMthat Continue on toPostpartum T2DM

Normal Weight Babies Bornfrom Non-GDM Mother with

History of GDM

Overweight Babies Born fromNon-GDM Mother with

History of GDM

Normal Weight BabiesBorn from GDM

Pregnancy

Overweight Babies Born

from GDM Pregnancy

Overweight Babies Born toPregnant Normal Weight

Mothers

Overweight Babies Bornfrom Pregnant Overweight

Mothers

Normal Weight Babies Born to

Mothers without GDM

Normal Weight BabiesBorn from T2DM

Pregnancy

Pregnancy

Duration

<Birth Rate>

Normal Weight Babies Bornto Overweight Mothers

without GDM

Normal Weight

Deaths

Overweight

Deaths

T2DM Deaths

Deaths from Non-T2DMWomen with History of

GDM

Discrete Event

Modeling

Agent-Based

Modeling

Social Network Analysis

Decision Analysis

Multiple Model Types

System Dynamics

System Dynamics Supporting ABM •High level SD model drives global dynamics, which affects ABM dynamics •Deriving calibrated parameter estimates for low-level model •Focusing AB exploration

•SD within Agents: Stocks & flows drive continuous elements of agent evolution

•SD model is used to capture dynamics of lower interest population/infrastructure; ABM for the area of greatest interest •Qualitative diagramming of

–Interactions at a particular scale

–Hypothesized drivers underlying emergent behaviour

Discrete Event

Modeling

Agent-Based

Modeling

Social Network Analysis

Decision Analysis

Multiple Model Types

System Dynamics

Agent-Based Modeling in Support of SD •Cross-validating SD aggregation: Evaluating

importance of –Stratification by heterogeneities –Stochastics –Network dynamics

•Aggregated agent behavior drives some flows in higher-level SD model(s) •Giving insight into feedbacks to depict •Investigating specialized interventions

–e.g. Interventions that depend on individual history, network position, etc.

•Use to determine parameters for SD model

Hands on Model Use Ahead

Load Provided Model: CTL State Variable V4

Hands on Model Use Ahead

Load Provided Model: GriddedSystemDynamics

System Dynamics & Individual-Based Modeling

•Individual-based models can be created using –Traditional System Dynamics software

•Small populations: –Separate stocks for each individual –Hand-drawn connections

•Larger Populations –Subscripting stocks by population member –Binary network matrices

–Stock & flows in other dynamic modeling software •e.g. in AnyLogic (e.g., embedded in agents)

–System Dynamics methodology •Feedback-centric reasoning

•Process-based work

Network Embedded Individuals

Uninfected

Cells

Infected

Cells

Virus Load

Uninfected Cell

Replentishment

New Cell

InfectionsUninfected Cell

death

Infected Cell

Death

Virion Production

From Infected Cells

Virion Clearance

Uninfected Cell

Replentishment Rate

Mean Infected Cell

Lifetime

Mean Uninfected

Cell Lifetime

Mean Virion

Lifetime

Likelihood Density of

Infection by Single Virion

Per Infected CellVirion

Production Rate

Virion Production Rate

Per Contact Virions Rate1 Person

Mean Viral Load<Population Size>

Mean Uninfected

Cells

Mean Infected

Cells<Population Size>

<Population Size>

Mean of Viral Load

of Neighbors

CTLs

immune response to

infected cellsCTL turnover

CTL

responsiveness

Mean CTL

lifespan

infected cell death

by CTLs rate which infected cells

are killed by CTLs

Virion Production Rate if

Non Quantized Infection

Individual-Based Model in Vensim

All of these stocks & their associated flows are particular to the

Population member (via population-member subscripting)

Population-Member Subscripting

Example Interactions between Global & Local Levels

A Global Level (Aggregate, Cross Population) Factor!

Example Individual-Level Risk Factors An Individual-Level Risk Factor

Another Individual-Level Risk Factor (here, represented categorically, but we could Represent it as a continuous variable – e.g. cumulative smoke exposure, some estimate of cumulative physiologic damage from smoke, a moving average of smoke exposure, etc.)

Impact of Risk Factors on Individual Dynamics

Discrete Event

Modeling

Agent-Based

Modeling

Social Network Analysis

Decision Analysis

Multiple Model Types

System Dynamics

Agent-Based Modeling in Support of DES

•Representing network of individuals in population outside of flow process

–Prior to entry (development of conditions) –Following exit (e..g trajectory dependent on quality of care) –Routing inflowing agents process based on agent’s history of care

–e.g. representing “catchment basin” of care facility

ABM & DES

Hands on Model Use Ahead

Load Provided Model: HybridABMNetworkModeling1

Discrete Event

Modeling

Agent-Based

Modeling

Social Network Analysis

Decision Analysis

Multiple Model Types

System Dynamics

SNA Can Facilitate ABM

•Social network statistics that be used to formulate synthetic networks •Identify patterns for calibration & investigation

•Cross-checks on ABM simulation findings •Network visualization

•Highlighting diverse settings for contact

Challenges in Using Data from SNA in ABM

•SNA can provide an extremely valuable source of data to use for grounding ABM network structure

•It is relatively easy to get networks from software like Pajek into software like AnyLogic or Repast •The bigger issue here is that we need to represent the hypothesized “true” spread of infection over the network

–To do this, we need to represent the hypothesized underlying network that lies behind

–Even the best of SNA data is highly incomplete (e.g. due to asymmetries in case-contact data, sampling in snowball sampling)

SNA Providing Context For ABM

Example Network Structure

Discrete Event

Modeling

Agent-Based

Modeling

Social Network Analysis

Decision Analysis

Multiple Model Types

System Dynamics

Agent-Based Modeling Facilitates SNA

•Exploring dynamic hypotheses to explain SNA patterns •Formulating ideas for SNA metrics that could be •highly effective (discriminatory) for identifying at-risk individuals •Understanding dynamic implications of given network structure

•Understanding implications of changing network structure

•Evaluating SNA-informed interventions (e.g. SNA-metric prioritized contact tracing) •Examining impact of additional collection of SNA data (e.g. , more complete contact tracing) •Positing possible pieces of missing structure in SNA network

ABM To Explain Emergent Patterns Uncovered via SNA

A.Al-Azem, Social Network Analysis in Tuberculosis B.Control Among the Aboriginal Population of Manitoba2006

Discrete Event

Modeling

Agent-Based

Modeling

Social Network Analysis

Decision Analysis

Multiple Model Types

System Dynamics

36

Two Relevant Methodologies

•Decision Analysis –Good for decision problems under uncertainty w/known scenario consequences

•No endogenous means of determining consequences

–Characterizes structured policy space –Sophisticated statistical tools & Sensitivity analyses typical –Identification of robust strategies via backwards induction –Discrete

•Events/decisions •Time

•Dynamic Modeling –Good for representing complex system response to scenario (events and actions) –Policy representation

•Highly flexible •Less structured policy space

–Basic statistical tools –Potentially continuous

•Time •Events/decisions

37

Decision Tree To Structure Policy Space

High later growth

PLConsequence1

Low later growth

1-PLConsequence2

Expand capacity

High later growth

PLConsequence3

Low later growth

1-PLConsequence4

No expansion

High early growth

PE

High later growth

PLConsequence5

Low later growth

1-PLConsequence6

Expand capacity

High later growth

PLConsequence7

Low later growth

1-PLConsequence8

No expansion

Low early growth

1-PE

Expand capacity

High later growth

PLConsequence9

Low later growth

1-PLConsequence10

Expand capacity

High later growth

PLConsequence11

Low later growth

1-PLConsequence12

No expansion

High early growth

PE

High later growth

PLConsequence13

Low later growth

1-PLConsequence14

Expand capacity

High later growth

PLConsequence15

Low later growth

1-PLConsequence16

No Expansion

Low early growth

1-PE

No expansion

Initial Decision

Time

Decision node

Event node

Terminal Node (Consequence for Scenario)

Scenario

38

Computed By System

Dynamics Model

Backwards Induction

•Run SD model to determine set of (preference-adjusted) outcomes for all terminal nodes •Compute expected value & risk profiles at event nodes •At decision nodes, choose decision with highest value

•FAST

(PL*Consequence1+(1-PL)*Consequence2)

(PL*Consequence3+(1-PL)*Consequence4)

High later growth

PLConsequence1

Low later growth

1-PLConsequence2

Expand capacity

High later growth

PLConsequence3

Low later growth

1-PLConsequence4

No expansion

High early growth

PE

High later growth

PLConsequence5

Low later growth

1-PLConsequence6

Expand capacity

High later growth

PLConsequence7

Low later growth

1-PLConsequence8

No expansion

Low early growth

1-PE

Expand capacity

High later growth

PLConsequence9

Low later growth

1-PLConsequence10

Expand capacity

High later growth

PLConsequence11

Low later growth

1-PLConsequence12

No expansion

High early growth

PE

High later growth

PLConsequence13

Low later growth

1-PLConsequence14

Expand capacity

High later growth

PLConsequence15

Low later growth

1-PLConsequence16

No Expansion

Low early growth

1-PE

No expansion

Initial Decision

Backwards Induction

39

Sensitivity Analysis •Offline sensitivity of likelihood impact on strategy selection

•Offline analysis (including Monte Carlo) of impact of likelihood change on risk profiles

Individual-Based Modeling in Vensim Population Subscripting Tradeoffs Advantages

•Conceptually simple

•Can SD tools –State trajectory file recording

–Easy construction, structure visualization

•No programming

–Sensitivity analysis –Easy to aggregate

Disadvantages

•Difficult to visualize network structure & spread or spatial embedding

•Awkward to realize changing population size